Importance sampling simulation methods for recursive and non-recursive symbol-by-symbol detectors

At the multiplexer of an ATM network, the admissible cell loss probability is less than 10−12 for some service categories. Ordinary Monte Carlo (MC) simulation requires considerable computation time to obtain such a small probability. The importance sampling (IS) technique is effective in accclerating the MC simulation. In an IS simulation, the underlying distribution is biased so as to generate more samples in the target event. In order to achieve a fast simulation, it is important to have a simulation distribution that yields an estimate with minimum variance. This is called the optimal simulation distribution. In this paper, we investigate the survivor function P(Q > q) of a stationary queue length Q in ATM queuing and obtain an IS estimate of P(Q > q) at about 10−2 by means of the optimal simulation distribution. Conventional methods [1, 2] for determining the optimal distribution require a lot of computation time. We apply the large deviation theory to this problem to obtain the optimal simulation distribution analytically and carry out an IS simulation. We present some numerical results for M/D/1 and 2-state MMPP/D/1 which demonstrate that our estimates are obtained in a very small computation time and are accurate when compared to MC simulation. © Scripta Technica, Inc. Electron Comm Jpn Pt 1, 80(12): 28–37, 1997

In this paper, the modification of conditional Fuzzy C-Means (CFCM) aimed at estimation of unknown desired channel states is accomplished for Bayesian blind channel equalizer under the presence of heavy additive Gaussian noise (AWGN). For the modification of CFCM to search the optimal channel states of a heavy noise-corrupted communication channel, a Gaussian weighted partition matrix, along with the Bayesian likelihood fitness function and the conditional constraint of ordinary CFCM, is developed and exploited. In the experiments, binary signals are generated at random and transmitted through both types of linear and nonlinear channels which are corrupted with various degrees of AWGN, and the modified CFCM estimates the channel states of those unknown channels. The simulation results, including the comparison with the previously developed algorithm exploiting the ordinary CFCM, demonstrate the effectiveness of proposed modification in terms of accuracy and speed, especially under the presence of heavy AWGN. Therefore, the proposed modification can possibly constitute a search algorithm of optimal channel states for Bayesian blind channel equalizer in severe noise-corrupted communication environments.

Modified efficiency importance sampling (MEIS), an importance sampling technique which can be used to yield a significant saving of run time for the assessment of bit error rate (BER) in digital communication systems using computer simulation, is described. The concept of equivalent noise source is introduced to avoid the effect of system memory on the efficiency of importance sampling, and a nonGaussian probability density function (p.d.f.) is selected as the biased equivalent noise to further improve run time. MEIS has been used successfully in the simulation of M-ary quadrature amplitude modulation (MQAM) systems. The MEIS is shown to be effective in the simulation of systems with large memory length, and in mildly nonlinear systems. The experimental results show that MEIS is a great improvement over Monte Carlo (MC) methods and that is even more efficient than the efficient importance sampling (EIS) technique. >

The authors extend the formulation for both classical Monte Carlo (MC) and importance sampling (IS) techniques to include the bit error rate (BER) and symbol error rate (SER) of multilevel systems based on symbol by symbol observation. A new IS technique and analysis of BER and SER based on the extended formulation are presented. The authors briefly summarize the previous work on BER of binary systems. The extended formulation is then presented. The conventional IS technique for BER of binary systems is shown to be applicable in simulating BER and SER of M-ary systems, and a new improved IS technique is presented. Numerical results for all the methods are provided. >

In this paper, we develop the use of an adaptive Importance Sampling (IS) technique in neural network training, for applications to detection in communication systems. Some topics are reconsidered, such as modifications of the error probability objective function (Pe), optimal and suboptimal IS probability density functions (biasing density functions), and adaptive importance sampling. A genetic algorithm was used for the neural network training, having utilized an adaptive IS technique for improving Pe estimations in each iteration of the training. Also, some simulation results of the training process are included in this paper.

In this paper, we present a variance minimization (VM) procedure for rare event simulation in tandem queueing networks. We prove that the VM method can produce a zero variance. The VM method is suitable to compute optimal importance sampling (IS) parameters for small scale tandem networks. For large scale tandem networks we propose a sub-optimal IS (SOIS) method, which projects the optimal biased transition probabilities of the corresponding small scale system into those of a large scale system. In other words, we establish an efficient IS method for a large scale system by zooming into a small scale system and then projecting our findings into the large scale system. The numerical results show that our SOIS method can produce accurate results with very short CPU time, while many other methods often require much longer.

This dissertation focuses on the importance sampling (IS) variance reduction technique in the Monte Carlo simulation of the performance of digital communication systems over a memoryless, additive Gaussian noise channel. The result is a unbiased estimate of the decision error with significantly smaller estimation variance than conventional Monte Carlo simulation provides. Several common digital (n, k) block codes are used to illustrate the importance sampling approach. Bounds on the variance of the error estimate are developed where the channel description is simple, but where the multiple dimension decision regions are potentially complex. Coherent detection is used as a venue for the comparison of these IS techniques with respect to increasing dimension. Bounds based on the union bound are presented for several IS techniques. An overlap stratification variance reduction technique is introduced and extended with the application of IS. A mixed IS biasing function is employed for concentrating more samples in a particular error region and is employed for several of the common lower rate ([special characters omitted] < 1) block codes. For the random phase channel the IS biasing function is developed as a 2n dimensional pdf consisting of n Rayleigh-Rician pdf pairs. The error performance of several common lower rate block codes is presented. An alternate formulation, having the potential advantage of being able to use both mean translation and variance scaling, is presented. This approach is based on a commonly used technique to numerically generate a single Rayleigh-Rician pdf pair.

The paper is dealing with estimation of rare event probabilities in stochastic networks. The well known variance reduction technique, called Importance Sampling (IS) is an effective tool for doing this. The main idea of IS is to simulate the random system under a modified set of parameters, so as to make the occurrence of the rare event more likely. The major problem of the IS technique is that the optimal modified parameters, called reference parameters to be used in IS are usually very difficult to obtain. Rubinstein (Eur J Oper Res 99:89–112, 1997) developed the Cross Entropy (CE) method for the solution of this problem of IS technique and then he and his collaborators applied this for estimation of rare event probabilities in stochastic networks with exponential distribution [see De Boer et al. (Ann Oper Res 134:19–67, 2005)]. In this paper, we test this simulation technique also for medium sized stochastic networks and compare its effectiveness to the simple crude Monte Carlo (CMC) simulation. The effectiveness of a variance reduction simulation algorithm is measured in the following way. We calculate the product of the necessary CPU time and the estimated variance of the estimation. This product is compared to the same for the simple Crude Monte Carlo simulation. This was originally used for comparison of different variance reduction techniques by Hammersley and Handscomb (Monte Carlo Methods. Methuen & Co Ltd, London, 1967). The main result of the paper is the extension of CE method for estimation of rare event probabilities in stochastic networks with beta distributions. In this case the calculation of reference parameters of the importance sampling distribution requires numerical solution of a nonlinear equation system. This is done by applying a Newton–Raphson iteration scheme. In this case the CPU time spent for calculation of the reference parameter values cannot be neglected. Numerical results will also be presented.

This paper illustrates the use of the Importance Sampling (IS) technique for efficient simulation of Orthogonal Frequency Division Multiplexing Systems operating over frequency selective fading channels with equalization. In order to achieve higher estimator variance reduction gains, the proper biasing procedure for time domain noise density function and the way of un-biasing the error count at the receiver in frequency domain are shown. Further, the optimum biasing parameters for conventional importance sampling (CIS) and improved importance sampling (IIS) methods are obtained. It is demonstrated, through simulations, that the proposed methods can provide extensive gains in estimator variance reduction and runtime saving compared to the conventional Monte-Carlo (MC) simulations.

We show that the importance sampling technique can effectively augment the range of problems where the nuclear ensemble approach can be applied. A sampling probability distribution function initially determines the collection of initial conditions for which calculations are performed, as usual. Then, results for a distinct target distribution are computed by introducing compensating importance sampling weights for each sampled point. This mapping between the two probability distributions can be performed whenever they are both explicitly constructed. Perhaps most notably, this procedure allows for the computation of temperature dependent observables. As a test case, we investigated the UV absorption spectra of phenol, which has been shown to have a marked temperature dependence. Application of the proposed technique to a range that covers 500 K provides results that converge to those obtained with conventional sampling. We further show that an overall improved rate of convergence is obtained when sampling is performed at intermediate temperatures. The comparison between calculated and the available measured cross sections is very satisfactory, as the main features of the spectra are correctly reproduced. As a second test case, one of Tully's classical models was revisited, and we show that the computation of dynamical observables also profits from the importance sampling technique. In summary, the strategy developed here can be employed to assess the role of temperature for any property calculated within the nuclear ensemble method, with the same computational cost as doing so for a single temperature.

Simulation is widely used to estimate losses due to default and other credit events in financial portfolios. The accurate measurement of credit risk can be modeled as a rare event simulation problem. While Monte Carlo simulation is time-consuming for rare events, importance sampling techniques can effectively reduce the simulation time, thus improving simulation efficiency. This chapter proposes a new importance sampling method to estimate rare event probability in simulation models. The optimal importance sampling distributions are derived in terms of expectation in the normal copula model developed in finance. In the normal copula model, dependency is introduced through a set of common factors of multiple obligors. The intriguing dependence between defaults of multiple obligors imposes hurdles in simulation. The simulated results demonstrate the effectiveness of the proposed approach to solving the portfolio credit risk problem.

Space-time block codes from orthogonal designs proposed by Alamouti, and Tarokh-Jafarkhani-Calderbank have attracted much attention lately due to their fast maximum-likelihood (ML) decoding and full diversity. However, the maximum symbol transmission rate of a space-time block code from complex orthogonal designs for complex constellations is only 3/4 for three and four transmit antennas. Recently, Jafarkhani,and Tirkkonen-Boariu-Hottinen proposed space-time block codes from quasi-orthogonal designs, where the orthogonality is relaxed to provide higher symbol transmission rates. With the quasi-orthogonal structure, these codes still have a fast ML decodng algorithm, but do not have the full diversity. The performance of these codes is better than that of the codes from orthogonal designs at low SNR, but worse at high SNR. This is due to the fact that the slope of the BER-SNR curve depends on the diversity. In this paper, we design quasi-orthogonal space-time block codes with full diversity by properly choosing the signal constellations. In particular, we propose that half of the symbols in a quasi-orthogonal design are from a signal constellation Α and another half of them are optimal selections from the rotated constellation ejφΑ . The optimal rotation angles φ are obtained for some commonly used signal contellations. The resulting codes have both full diversity and fast ML decoding. Simulation results show that the proposed codes outperform the codes from orthogonal designs at both low and high SNRs.© (2002) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Vehicle routing problem belongs to classical Combination Optimization hard problem and has been extensively studied by many researchers. Vehicle Routing Problem with Weight Coefficients and Stochastic Demands (WVRPSD) is established and a new implementation for importance sampling method to solve this model is proposed in this paper, in which the classical exponential change of measure is adopted to construct the family of importance sampling distributions, and the optimal importance sampling distribution is obtained by minimizing the variance of importance sampling estimator. Numerical experiments have been conducted and the results indicate that the method can effectively solve this problem.

B-ISDN networks based on asynchronous transfer mode (ATM) are characterized by very low cell loss probability. This results in an enormous computational burden when determining the system's performance via Monte Carlo simulation. To improve the computational efficiency different methods (for example Restart and GEVT) have been proposed in literature to evaluate the occurrence of rare events. We show how importance sampling (IS) allows one to obtain useful results in this field. While IS techniques have been largely exploited in the evaluation of bit error rate in digital communication systems and of false alarm rate in radar devices very little has been done to develop efficient IS-based schemes to simulate a queueing system fed with self-similar traffic. With this work we show how IS may be applied to simulate a queue fed both with fractional Gaussian noise (FGN) and with synthetic traces with characteristics close to the ones of real traffic, resulting from videoconferencing sessions.

Estimating the distribution of total default losses on the Spanish financial system